Comparison of various shear deformation theories for the free vibration of thick isotropic beams

In this paper, a comparative study of refined beam theories has been done for the free vibration analysis of thick beams, taking into account transverse shear deformation effect. The theories involves parabolic, sinusoidal, hyperbolic and exponential functions interms of thickness coordinates to include transverse shear deformation effect. The numbers of unknowns are same as that of first order shear deformation theory. The governing differential equations and boundary conditions are obtained by using the principle of virtual work. The results of bending and thickness shear mode frequencies for simply supported beam are presented and discussed critically with those of other theories. The results are found to agree well with the exact elasticity results wherever applicable. Comparison of dynamic shear correction factor is carried out using various shear deformation theories.